an approach for the estimation of the aggregated …...y.-m. saint-drenan et al.: estimation of the...

Adv Sci Res 15 51ndash62 2018httpsdoiorg105194asr-15-51-2018copy Author(s) 2018 This work is distributed underthe Creative Commons Attribution 40 License

17thE

MS

AnnualM

eetingEuropean

Conference

forApplied

Meteorology

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limatology

2017

An approach for the estimation of the aggregatedphotovoltaic power generated in several European

countries from meteorological data

Yves-Marie Saint-Drenan1 Lucien Wald1 Thierry Ranchin1 Laurent Dubus24 and Alberto Troccoli34

1MINES ParisTech PSL Research University OIE ndash Centre ObservationImpacts Energy 06904 Sophia Antipolis France

2EDF RampDMFEE Applied Meteorology and Atmospheric Environment CHATOU CEDEX France3School of Environmental Sciences University of East Anglia Norwich NR4 7TJ UK

4World Energy amp Meteorology Council (WEMC) Norwich NR4 7TJ UK

Correspondence Yves-Marie Saint-Drenan (yves-mariesaint-drenanmines-paristechfr)

Received 16 January 2018 ndash Revised 2 April 2018 ndash Accepted 6 April 2018 ndash Published 2 May 2018

Abstract Classical approaches to the calculation of the photovoltaic (PV) power generated in a region frommeteorological data require the knowledge of the detailed characteristics of the plants which are most often notpublicly available An approach is proposed with the objective to obtain the best possible assessment of powergenerated in any region without having to collect detailed information on PV plants The proposed approach isbased on a model of PV plant coupled with a statistical distribution of the prominent characteristics of the con-figuration of the plant and is tested over Europe The generated PV power is first calculated for each of the plantconfigurations frequently found in a given region and then aggregated taking into account the probability of oc-currence of each configuration A statistical distribution has been constructed from detailed information obtainedfor several thousands of PV plants representing approximately 2 of the total number of PV plants in Germanyand was then adapted to other European countries by taking into account changes in the optimal PV tilt angle as afunction of the latitude and meteorological conditions The model has been run with bias-adjusted ERA-interimdata as meteorological inputs The results have been compared to estimates of the total PV power generated intwo countries France and Germany as provided by the corresponding transmission system operators RelativeRMSE of 42 and 38 and relative biases of minus24 and 01 were found with three-hourly data for France andGermany A validation against estimates of the country-wide PV-power generation provided by the ENTSO-Efor 16 European countries has also been conducted This evaluation is made difficult by the uncertainty on theinstalled capacity corresponding to the ENTSO-E data but it nevertheless allows demonstrating that the modeloutput and TSO data are highly correlated in most countries Given the simplicity of the proposed approach theseresults are very encouraging The approach is particularly suited to climatic timescales both historical and futureclimates as demonstrated here

1 Introduction

Time series of photovoltaic (PV) power generated within aregion are needed for prospective studies on the transfor-mation of the electricity supply system Under classical ap-proaches an accurate calculation of the power generated byPV plants in a region requires the knowledge of the detailedcharacteristics of the plants A few cases can be found where

enough information is available and can be used for themodel development andor validation (see eg Jamaly et al2013 Lingfors and Wideacuten 2016 Shaker et al 2015 2016)Plant production data are however most often unavailableto the public They may be collected from eg the opera-tors of PV plants but this represents a huge amount of workHence an accurate calculation of the PV power generated inany European region with a classical method represents an

Published by Copernicus Publications

52 Y-M Saint-Drenan et al Estimation of the PV power generation in several EU countries

exhaustive and time-consuming task and is intractable Al-ternatively statistical approaches may be used to train mod-els from historical time series of the aggregated PV gener-ated power such as those published by the transmission sys-tem operators In this case the collection understanding andquality check of the training data is primordial to ensure ac-curate model output Though more practical than the clas-sical approaches these statistical approaches are also timeconsuming because of the handling of the data and they can-not be applied in regions where no training data is avail-able Another common practice consists in estimating thetotal power generated in a region by upscaling the powergenerated by a subset of reference plants (Schierenbeck etal 2010 Lorenz and Heinemann 2012 Shaker et al 20152016 Saint-Drenan et al 2016 Bright et al 2017 Pierro etal 2017 Killinger et al 2017) The major obstacles to thispractice is on the one hand the establishment of criteria onthe selection of the plants that are statistically representativeof the region and their number and on the other hand theaccess to measurements of the selected plants In additionthose methods only allow estimating the PV power gener-ation for historical periods where measurements are avail-able and their extrapolation to other periods is not straight-forward This can be a major drawback for eg generationadequacy study or prospective analysis where scenarios withlong time series are needed A further option consists in se-lecting a simple PV model with a very limited number ofunknowns (Jerez et al 2015) whose implementation for anyregion is easy to do at the expense of the model accuracy Fi-nally several authors propose to consider a mix of differentkey parameters where the distributions are chosen by the au-thors (Marinelli et al 2015 Schubert 2012) This requiresa deep expertise of the domain This approach is limited to afew regions and cannot be used to model all EU countries

This brief survey of the proposed approaches demon-strates the need for a new approach that offers a bettertrade-off between implementation constraints and model out-put accuracy This paper describes a method addressing thisneed It has been developed in the framework of the EU-funded Copernicus Climate Change Service ECEM1 (Euro-pean Climate Energy Mixes) project which aims at produc-ing in close collaboration with prospective users a proof-of-concept climate service or demonstrator whose purposeis to enable the energy industry and policy makers to assesshow well different energy supply mixes in Europe will meetdemand over different time horizons (from seasonal to long-term decadal planning) focusing on the role climate has onthe mixes (Troccoli et al 2017)

The innovation of our method is the extension of theregional PV model proposed by Saint-Drenan (2015) andSaint-Drenan et al (2017) to any region without the needfor a priori knowledge of the characteristics of the installedPV plants To this end the plant-related parameters which

1httpecemclimatecopernicuseu

are needed as input to the PV model are expressed as a func-tion of known solar resource characteristics making thus themodel generalizable to any region namely beyond Germanywhere the approach was originally tested This is achieved intwo steps firstly by reducing the number of inputs to the PVmodel by the means of an analytical function for the statis-tical distribution of the module orientation and secondly byexpressing the parameters of the chosen analytical functionsas a function of known geographically-dependent informa-tion (optimal tilt angle)

The paper is organized as follows After a short summaryof the regional PV model proposed by Saint-Drenan (2015)and Saint-Drenan et al (2017) in Sect 21 the reduction ofthe number of parameters achieved by the use of an ana-lytical function is detailed in Sect 22 The approach cho-sen to relate the parameters of the analytical function toknown geographically-dependent quantities is then explainedin Sect 23 Implementation details are provided in Sect 24The results of a validation of the model are described inSect 3 where the model output has been compared to es-timates of the total PV power generation of France and Ger-many provided by transmission system operators (TSOs) Fi-nally the results and potential improvements of the approachpresented are discussed in Sect 4

2 Approach

Our approach for modelling the PV power generation in anycountry use a generic PV model which needs only the distri-bution of the two module orientation angles as inputs Thismodel is introduced in Sect 21 and the methodology for es-timating the distribution of the module orientation angles inany location is described in the Sect 22 and 23 Finallysome implementation details are given in Sect 24

21 Description of the model for the aggregated PVpower produced in a region

The proposed method is built upon previous works by Saint-Drenan (2015) and Saint-Drenan et al (2017) where a modelfor the aggregated PV power produced by a fleet of PV plantsinstalled in a region is described The authors have showedthat an accurate estimate of the German PV power genera-tion can be obtained by using the statistical distribution ofthe orientation angle of PV panels as the sole plant-relevantinput to the model (Fig 1) The model is based on the simpleidea that the aggregated PV power generated in a region isthe sum of the normalized outputs of all plants with charac-teristics Ai multiplied by the proportion wi of plants havingthe characteristics Ai in the whole set of plants installed inthe considered region The regional PV power generation cantherefore be expressed as follows

PPV(xt)=nsumi=1

wi fPV (x tG(x t) Ta (x t) Ai) (1)

Adv Sci Res 15 51ndash62 2018 wwwadv-sci-resnet15512018

Y-M Saint-Drenan et al Estimation of the PV power generation in several EU countries 53

Figure 1 Flow chart of the single PV plant model

Where PPV(x t) is an estimate of the aggregated power pro-duced by all PV plants located at x at time t [W Wminus1

p ]G(x t) is the global horizontal irradiance (GHI) received atx and t [W mminus2] Ta (x t) is the air temperature at x and t[C] fPV( ) is a function representing the single PV plantmodel used to calculate the normalized PV power [W Wminus1

p ]A first advantage of the chosen regional PV model is that

each important configuration is considered only once and thenumber of configurations Ai can be optimized in order tolimit the calculation costs A second advantage is the highflexibility offered by the use of an analytical function to de-scribe the statistical distribution of the characteristics of theplants installed in a region

The function fPV in Eq (1) represents a single plantmodel which needs to be chosen prior to the implementationof the proposed approach In Saint-Drenan (2015) and Saint-Drenan et al (2017) the authors demonstrated that a simplemodel with a limited number of input parameters yields goodresults for regional application With the chosen model theset of characteristics Ai is only composed of the module tiltangle γ and azimuth angle α or orientation The Airsquos whichare a function of (α γ ) are hereafter referred to as referenceconfigurations There are two steps for the implementationof the regional PV model that are described in the follow-ing section the estimation of the weights wi and the choiceof the reference configurations A detailed description of thechosen model which is illustrated in Fig 1 can be found ineg (Saint-Drenan 2015)

22 Modelling the weights wi

Saint-Drenan (2015) and Saint-Drenan et al (2017) have cre-ated a dataset of peak power and module orientation anglesfor 35 000 PV plants located in Germany which is used hereThis amount of plants represents approximately 2 of thenumber of plants installed in Germany It is assumed that this

Figure 2 Share of the installed capacity per module orientationevaluated from the 35 000 PV plants installed in Germany (colouredsquares) Black squares denote the set of 19 reference orientationsused for the implementation of the regional model

dataset is representative of all plants in Germany A realisticexample of the relationship between wi and Ai at countrylevel may be derived from this dataset Figure 2 exhibits theshare wi of installed capacity per module orientation evalu-ated from this dataset One may note the high share of in-stalled capacity for modules with a tilt of 20 southwardsfacing (orientation 180)

The use of Eq (1) requires that the space spanned by αand γ is properly sampled in order to obtain a robust esti-mation of the plant shares wi corresponding to the sampledorientations Ai = (αiγi) in that equation The smoothnessand form of the joint distribution displayed in Fig 2 suggestthat it may be possible to fit an analytical relationship there-fore reducing the number of parameters used to describe itWe propose to use the product of two Gaussian distributions

wi (αiγi)=

[1radic

2πσ 2α

exp

(minus

(αi minusmicroα)2

2σ 2α

)] 1radic

2πσ 2γ

exp

(minus

(γi minusmicroγ

)22σ 2γ

) Ai = (αiγi) (2)

In Eq (2) the first product term corresponds to the normaldistribution of α characterised by a mean value microα and astandard deviation σα The second product term correspondsto the normal distribution of γ characterised by a mean valuemicroγ and a standard deviation σγ It appears reasonable to as-sume that the distribution of α is centred on a southwardsorientation so that microα can be set to 180 In Eq (2) it isassumed that the distributions of the α and γ are indepen-dent ndash from Fig 2 this assumption is an acceptable first-orderapproximation A different notation has been used for the

wwwadv-sci-resnet15512018 Adv Sci Res 15 51ndash62 2018


Figure 3 Comparison of the experimental histograms of two mod-ule orientation angles (blue bars) with the fitted normal distributionfunction (red lines) for the module azimuth angle (a) and the mod-ule tilt angle (b) N(180 193) (a) means that the average orientationis 180 and the standard deviation is 193 N(206 108) (b) meansan average tilt angle of 206 and a standard deviation of 108

weights wi in Eqs (1) and (2) since as further explained inSect 5 values wi calculated with Eq (2) must be normalizedbefore being inserted into Eq (1)

The use of the analytic form in Eq (2) for the weightswi allows reducing the number of plant-relevant parametersdown to three which are the mean and standard deviationof γ and the standard deviation of α This reduced form hasbeen tested using the German solar plants We found an av-erage value of 206 for microγ and values of 193 and 108

for σα and σγ The empirical histograms of the tilt and az-imuth angles are compared to their fitted normal distributionsin Fig 3 The match between the histograms is not perfect butit seems an acceptable first-order approximation

23 Parameterisation of the relationship between thedistribution of the orientation of PV modules and thegeographical location

The three plant-related parameters necessary to calculate thetotal PV power produced in a given region from meteoro-logical data has been determined above in the specific caseof Germany How can these three parameters be extended toother countriesregions At this stage one possibility mayconsist in using ones own expertise on the characteristics ofPV plants installed in the considered regions as in Marinelliet al (2015) Schubert (2012) another is a detailed statisti-cal analysis of a dataset of plant information installed in thestudied areas Both ways hamper the easy use of the regionalmodel aimed at in this work To address this issue a parame-terization of the three parameters is proposed in this sectionwhich makes the model implementable in any region withoutany prior knowledge on the installed PV plants

The statistical distribution of the plant capacity as a func-tion of the module orientation of a region is the result of in-dividual choices on the configurations of each single plantIt is affected by many factors of different nature such as

Figure 4 (a) Optimal tilt angles taken from the PV-GIS website(httprejrceceuropaeupvgis) (b) Optimal tilt angles used forthe present work where high values present in mountainous regionshave been filtered out

the characteristics of the solar resource the shading pro-file architectural characteristics different installation prac-tices etc All these factors cannot be taken into considera-tion and we make the assumption that the most importantone is the characteristics of the solar resource We proposeto take this into consideration through the use of an opti-mal tilt angle The optimal tilt angle corresponds to the valueof the tilt angle of a southwards oriented module yieldingthe largest annual output In this work we use the rasterfile of optimal tilt angles available on the PV-GIS web-site (httprejrceceuropaeupvgis) which is displayed inFig 4a as our starting point

It can be observed in Fig 4 that the optimal tilt angle γoptis ranging between 30 and 35 in Germany while the averagevalue for the tilt angle has been found equal to 206 in theprevious section The reason for this mismatch is that a tiltangle smaller than the optimal tilt angle is commonly usedto install more PV capacity per unit of surface and maximizethe economic output of the plant This practice has becomemore frequent with decreasing PV price and scarce avail-able surfaces for new installations We propose to quantifythe mismatch between these two angles by a coefficient f The average tilt angle microγ can thus be expressed as

microγ = f γopt (3)

The unknown factor f can vary from one plant to anothersince it depends on numerous factors such as the solar re-source the plant cost per peak capacity or the land price Itmay thus exhibit spatial and time variation and an accuratedetermination of this coefficient for all European countriesmay be difficult We assume that this factor is spatially con-stant Considering the average value of the tilt angles whichis equal to 206 the factor f should be chosen between 06(20635) and 07 (20630) Given that the chosen dataset in-cludes an under-representative share of large solar park thatusually have an optimal tilt angle (Saint-Drenan 2015) wehave chosen the upper bound for f (f = 07) Similarly we



assume the standard deviations of the azimuth and tilt anglesspatially constant and set them to the values found with theset of PV plants installed in Germany (193 and 108 for theazimuth and tilt angle)

The weights corresponding to the different orientation an-gles are finally estimated using Eq (2) where the mean tiltangle is taken equal to the optimal tilt angle time the factorf = 07 and the standard deviations of the azimuth and tiltangles are considered constant and equal to 193 and 108

respectively

24 Implementation details

Some implementation details have been intentionally omit-ted in the previous sections for the sake of clarity and con-ciseness This section provides some important details for theimplementation of our method

For the implementation of Eq (1) the identification of alimited number of vectors Ai describing the reference mod-ule orientations is necessary The accuracy of the model out-put and the computation cost will depend on the number ofvectors chosen It is thus an important step for an efficientuse of our model We used a set of 19 module orientationangles three azimuth angles (170 180 and 190) and 7 tiltangles ranging from 0 to 60 with a step of 10 These arerepresented by black squares in Fig 2

Our parameterization of the distribution of the module ori-entation is a function of the optimal tilt angle found on thePV-GIS website This dataset is displayed in the left map ofFig 4 where it can be observed that greater than average val-ues are present in mountains (see eg regions of the Alps orthe Pyrenees) These high values are presumably stemmingfrom the high irradiation values present at high elevationsSince little PV plants are installed in these regions and toavoid overestimation of the tilt angle in the region neigh-bouring the mountains these values have been filtered outThe resulting data are displayed in the right map of Fig 4

As already mentioned in Sect 3 the expression given inEq (2) cannot be directly used to estimate the weights wineeded by Eq (1) Indeed for a finite sample of orientationangles Ai the sum of the values wi evaluated with Eq (2) isnot equal to unity To address this issue wi estimated withEq (2) is normalized as follows to yield wi

wi =

intintDi

wi(αγ )dαdγ

sumi

(intintDi

wi(αγ )dαdγ

) with

Di =

[αi minus

δα

2 αi +

δα

2

]times

[γi minus

δγ

2 γi +

δγ

2

](4)

The scalars δα and δγ in Eq (6) represent respectively theresolutions of the azimuth and tilt angles which are bothequal to 10 in our implementation

Figure 5 Spatial distribution of the installed PV capacity in Franceand Germany for the year 2014 The installed capacity is aggregatedon the pixel used for the calaculation which have a resolution of05

3 Model evaluation

31 Evaluation methodology

The model has been assessed by comparing its outputs to thePV power generated within a country Given the approach isinfluenced by uncertainties in the input meteorological pa-rameters this comparison allows only an indirect evaluationof our model and not a quantification of the modelling accu-racy However this approach offers a good balance betweenaccuracy and versatility The goal of this evaluation is thusto verify the plausibility of the model output for a particularmodel set up Not only is there a lack of certainty in the in-put meteorological data but also there are various sources ofuncertainty impacting the TSO data as well as the installedcapacity used by the model both making the conclusion ofthe validation difficult To address these issues we conductthe validation in two steps In the first step the validation isconducted for two countries France and Germany where wehave long experience with both the installed capacity and theTSO data In this first step the impact of the uncertainty onthe installed capacities and TSO estimates is under controlbut its spatial extension is limited We therefore conduct asecond step where TSO data from 16 countries are consid-ered Given the lack of available information on the installedPV capacity in these countries it is assumed spatially andtemporally constant The actual installed capacity being un-



Figure 6 Comparison of the model output (blue lines) with TSO estimates (red lines) of the PV power generated in France (a) and Ger-many (b) The data are displayed over the year with a daily time resolution in the two plots above and for two example weeks in a 3-hourlytime resolution in the two lower plots

Figure 7 Scatter plots of the TSO data against model outputs for France (a) and Germany (b) for the calculation based on the spatiallyresolved installed capacity of the year 2014

known the validation is made by evaluating the correlationcoefficient between TSO data and model output

32 Detailed evaluation of the model output for Franceand Germany

The assessment is first performed for Germany and Francefor the year 2014 The choice of these two countries hasbeen strongly motivated by the comparatively high level ofknowledge of their electricity supply structure and the avail-ability of the data to conduct the validation The PV power

data was provided by the TSOs themselves with a time res-olution ranging from 15 min to 1 h A visual analysis of thetime series was performed to control the data The data wasaggregated into 3 h means to conform to the temporal resolu-tion of the meteorological data Instants with no productionby PV (night time) were excluded from the comparison

The German case is used to validate the assumption madethat the statistical quantities evaluated with 35 000 plants canbe generalized to the ca 1 500 000 plants installed in Ger-many at that time France has a different level of PV devel-



Figure 8 Histograms of the ratio of actual plant tilt angles with thecorresponding optimal value for different classes of nominal capac-ity (coloured lines) In the upper plot the German case is calculatedwith the IWES database The French case is displayed in the lowerplot where data from BDPV are used

opment compared to Germany and is located at slightly dif-ferent latitudes This second case will test the validity of ourapproach to generalize the statistical quantities evaluated inGermany to another country with somewhat different meteo-rological conditions

Gridded values of the normalized PV power were com-puted with the model using the bias-adjusted ERA-interimdata proposed by the ECEM project (Jones et al 2017) asmeteorological inputs A bias-adjusted dataset was preferredto the original ERA-Interim re-analysis dataset in order tolimit the effect of error in the input meteorological data on theassessment of model performance The bias-adjusted ERA-Interim covers the period from 1 January 1979 to 31 De-cember 2016 and is covering Europe with a spatial resolu-tion of 05times 05 The domain covered by the data extendsbetween 2175 and 4525 in longitude and between 2675and 7225 in latitude The two meteorological variables usedfor the calculation were the solar surface radiation downward(SSRD also known as GHI) and air temperature at 2 m Asthe input meteorological data has a time resolution of 3 h forSSRD and 6 h for temperature an increase of the time res-olution was needed to properly estimate the PV power gen-eration with respect to the variation of the sun position withtime For this purpose the temperature and clearness index(the ratio of SSRD to the irradiation at the top of atmosphere)were resampled down to a time resolution of 5 min by a lin-ear interpolation technique The normalized PV power wascalculated with these resampled inputs and then summed upon 3 h periods which is the original time resolution of thesolar radiation data

By using gridded maps of the installed PV capacity ineach country (Fig 5) the generated PV power was com-puted at each grid cell and then spatially summed to yieldthe production for each country The data on the installedPV plants used for this purpose have been retrieved from thewebsites of the four German TSOs (PV-DE 2014) and from adata portal of the French government (PV-FR 2014) Finallyall time series have been normalized by the total installedPV capacity which is equal to 617 and 3687 GWp forFrance and Germany respectively in 2014 (PV-DE 2014PV-FR 2014) Figure 6 exhibits the time series of both mea-sured production and model outputs for France and Germanydaily and 3 h resolutions It reveals that the seasonal vari-ations of the PV power are well assessed by the proposedmodel for the two countries and that the match betweenmodel output and actual values is qualitatively good Scat-ter plots of the TSO data against the model outputs are dis-played in Fig 7 for France and Germany for the 3 hourlyresolution and different error metrics are also displayed inFig 7 The data points are well centred on the identity linefor Germany while an underestimation by the model can beobserved for France These observations are confirmed bythe bias which are respectively equal to minus24times 10minus2 and01times10minus2 W Wminus1

p for France and Germany The correlationcoefficient is large in both countries 0987 and 0975 re-spectively for France and Germany The MAE is respectively38times10minus2 and 24times10minus2 W Wminus1

p the RMSE is respectively42times 10minus2 and 30times 10minus2 W Wminus1

p Some efforts were made to understand the reasons for the

greater bias value observed for France During this investiga-tion we obtained access to the content of the bdpvfr onlineportal (BDPV 2018) which contains the main informationfor more than 20 000 PV plants installed in France We usedthis new data source to compare the characteristics of theGerman and French PV plants and to verify the validity ofour assumption for France

The strongest assumption made in this work is to considerthat the mean tilt angle is equal to the product of the optimaltilt angle and a constant f equal to 07 In order to verifythis assumption the ratio between actual and optimal mod-ule tilt angle has been analysed for the two countries Thehistograms of this ratio are displayed for the two countriesand for different classes of nominal capacity in Fig 8 Theassumed value for the ratio f is displayed by a dashed blackline in these two plots We can observe that the assumed ra-tio value matches well large German plants with an installedcapacity greater than 500 kWp (no information on large PVplant is available in France) Data from both countries revealthat this value is not fitting actual tilt values of medium andsmall plants an optimal ratio value of 04ndash06 would bet-ter match plants with an installed capacity between 50 and500 kWp and a ratio value of 09ndash13 would be better forplants with an installed capacity smaller than 10 kWp It isinteresting to note that the optimal ratio changes with the size



Figure 9 Spatial distribution of the tilt angle for plants smaller than 25 kWp (a) and greater than 25 kWp

of the plants in a similar way for both countries These obser-vations indicate that the variation of the share of PV plantsaccording to their size between countries can bring about adeviation from the assumed factor of 07 A first possible ex-planation for bias observed in France may thus be that thedistribution of French plants according to their size is differ-ent from the German one

It would be interesting to exploit the trend observed inFig 8 in our model However information on the size of in-stalled PV plants is missing in most European countries sothat this is unfortunately impossible Based on these new re-sults one can wonder whether the choice of a value of 07for the ratio between actual and optimal tilt is still relevantGiven that larger plants have more weight for the calculationof the regional PV power generation than smaller plants weconsider that our estimate is not unfounded and we decide tokeep this value

In Fig 8 it can also be observed that for PV plants with aninstalled capacity smaller than 10 kWp the range of tilt an-gle values taken by French plants is larger than for Germanplants To understand this difference the tilt angle values ofsmall plants have been displayed as a function of their geo-graphic position (Fig 9) In this map a very large differencein tilt angles between North and South of France can be ob-served This spatial difference is much more pronounced thanthe spatial variation that can be expected from the optimal tiltangle Since such a marked spatial difference is not presentin Germany it could bed a second possible explanation to theobserved bias in France

As reported in Saint-Drenan (2015) the spatial variationsof the tilt angle of small plants are resulting from regionalarchitectural practices It would therefore be tempting to in-tegrate this information into our model However because

this information is not commonly available (ie not even forFrance) it could not be accounted for in a robust way

33 Model evaluation for all European countries

Though the results of this first validation can be considered assatisfactory it is important to also demonstrate that results forGermany and France can be extrapolated to other (European)countries also with different climates engineering practicesetc We therefore decided to conduct an additional validationstep in which we compared the output of our model to ad-ditional TSO data To this end we collected time series ofsolar power generation on the ENTSO-E Transparency Por-tal for 16 countries for the year 2015 and built 3-hourly aver-ages to make the data comparable with the model output Themodel setup is the same than in the previous validation exceptfor the installed capacity which is not known and thus as-sumed spatially and temporally constant (even in France andGermany) Indeed the information available on the installedcapacity is only updated yearly and we experiment severalsituations where the time series of the production were notmatching with the given installed capacity (eg situation withproduction values greater than the installed capacity)

The comparison of the model output with the ENTSO-Edata has been conducted for 16 countries The scatter plot ofthe model output against ENTSO-E data is given in Fig 10for each country As mentioned before since the installed ca-pacity is not known the model output has not been scaled tothe actual capacity As a result one should not consider theabsolute error values in these plots but solely the correlationbetween the two time series Accordingly only the correla-tion coefficient is given in Fig 10 and discussed in the re-maining of this section To facilitate the visualisation of the



Figure 10 Scatter plots of three-hourly ENTSO-E solar generation data against the corresponding model output for 16 European countriesfor the year 2016 The modelled PV generation has been calculated with ERA-interim data assuming a spatially constant installed capacity



Figure 11 Spatial distribution of the correlation between ENTSO-E data and model output for a three-hourly time resolution and forthe year 2016

results the correlation coefficients evaluated for the differentcountries are displayed as a map in Fig 11

With values greater than 097 the correlations are partic-ularly high in Italy France and Germany These results con-firm those obtained for France and Germany in the first vali-dation That the best correlation (0982) is found for Italy is avery good surprise since no information on the PV plants in-stalled in this country was considered in the model develop-ment As we can see in Fig 12 the high installed capacity inItaly (ca 19 GWp in 2016) may account for this good perfor-mance The correlation coefficients are high and comprisedbetween 095 and 097 for six countries Denmark BelgiumCzech Republic Slovakia Greece and Portugal This demon-strates that the proposed approach using the optimal tilt an-gle is valid at different latitudes The low performance of themodel for Spain is explained by the fact that the time series ofsolar generation available on the ENTSO-E website includesboth photovoltaic and concentrated solar power generationThe reason for the medium performance in the remainingcountries is unclear it may stem from an intra-yearly changeof the installed capacity from lower performance of the re-analysis data in some regions or from other unidentified is-sues including in the ENTSO-E generation data It is how-ever interesting to note that in the 16 countries as shown inFig 8 the greater the installed capacity the better the per-formance of our model performance There may be severalreasons to explain this observation firstly the relative effectof the intra-yearly new installations is lower when the in-stalled capacity is high and secondly our assumption on the

Figure 12 scatter plot of the correlation coefficients betweenmodel output and ENTSO-E data against installed PV capacity forthe 16 different countries

distribution of plants may only become valid as the numberof plants exceeds a certain threshold

4 Conclusions

This paper describes an innovative approach that offers atrade-off between implementation constraints and model out-put accuracy convenient for the goals of the C3S ECEMservice and that may be used in other contexts The vali-dation of the model against country-aggregated productionof electricity by PV plants for France and Germany showsthat the model is accurate enough with a RMSE of 3ndash4 of the installed capacity In addition the model has been fur-ther validated against solar power generation time series from16 countries which give correlation coefficient above 094except for 4 countries (Austria Lithuania Netherlands andSwitzerland) The reasons for the under-average scores forthese countries could unfortunately not be identified whichrepresents a first possible continuation of the present workThis validation revealed that the greater the installed capac-ity the better the performance of our model is This findingtogether with the satisfying results of our performance anal-ysis confirm that the proposed model is well suited for ourtargeted applications Indeed the goal of the present workwas not to make a perfect model for a single country but topropose a generalized approach that can be implemented inany (European) region without having to collect any specificinformation on the fleet of plants installed in that countryWe believe an under-optimal performance is thus acceptable



with respect to the gain in flexibility offered by the proposedapproach

Additional validation work would bring a better insightinto the strengths and weaknesses of the proposed method-ology and identify possible improvements In addition dataon PV production is available from TSOs in many Euro-pean countries and the validation may be performed for thesecountries thus confirming or not the performances of themodel presented here The model may be refined with re-spect to its parameters using more data from various coun-tries A possible approach to this end may consist in estimat-ing the probability function of the regional PV model usinginversion techniques using the optimal tilt angle dependentdistribution described in this paper as a first guess

Time series of PV power generation have been calculatedin the framework of the C3S ECEM service with the pro-posed approach using the ECEM bias-adjusted ERA interimdata and future climate projections for 33 countries in a 3 htime resolution These model output data are freely avail-able on the demonstrator of this project httpecemclimatecopernicuseudemo

Data availability The set of adjusted reanalysis data is avail-able on ESSD (Jones et al 2017) and has the following DOIhttpsdoiorg105194essd-9-471-2017 Times series of aggre-gated PV power generation are available at country level for all EUcountries on the following ftp server ftpecemclimatecopernicuseu

Competing interests The authors declare that they have no con-flict of interest

Special issue statement This article is part of the special issueldquo17th EMS Annual Meeting European Conference for Applied Me-teorology and Climatology 2017rdquo It is a result of the EMS AnnualMeeting European Conference for Applied Meteorology and Cli-matology 2017 Dublin Ireland 4ndash8 September 2017

Acknowledgements The authors would like to acknowledgefunding for the European Climatic Energy Mixes (ECEM) serviceby the Copernicus Climate Change Service a programme beingimplemented by the European Centre for Medium-Range WeatherForecasts (ECMWF) on behalf of the European Commission Thespecific grant number is 2015C3S_441_Lot2_UEA

Edited by Sven-Erik GryningReviewed by Sven Killinger Hans Georg Beyerand one anonymous referee

References

BDPV Information from a set of ca 20 000 PV plants installed inFrance httpwwwBDPVfr last access February 2018

Bright J M Killinger S Lingfors D and Engerer N AImproved satellite-derived PV power nowcasting using real-time power data from reference PV systems Sol Energyhttpsdoiorg101016jsolener201710091 in press 2017

Jamaly M Bosch J and Kleissl J Aggregate Ramp Rates Anal-ysis of Distributed PV Systems in San Diego County 4 519ndash5262013

Jerez S Thais F Tobin I Wild M Colette A Yiou P andVautard R The CLIMIX model A tool to create and evalu-ate spatially-resolved scenarios of photovoltaic and wind powerdevelopment Renewable and Sustainable Energy Reviews 421ndash15 httpsdoiorg101016jrser201409041 2015

Jones P D Harpham C Troccoli A Gschwind BRanchin T Wald L Goodess C M and Dorling S Us-ing ERA-Interim reanalysis for creating datasets of energy-relevant climate variables Earth Syst Sci Data 9 471ndash495httpsdoiorg105194essd-9-471-2017 2017

Killinger S Guthke P Semmig A Muumlller B Wille-HaussmannB and Fichtner W Upscaling PV Power Considering ModuleOrientations IEEE J Photovoltaics 7 941ndash944 2017

Lingfors D and Wideacuten J Development and validation of a wide-area model of hourly aggregate solar power generation Energy102 559ndash566 2016

Lorenz E and Heinemann D Prediction of Solar Irradiance andPhotovoltaic Power in Comprehensive Renewable Energy 1239ndash292 httpsdoiorg101002pip1224 2012

Marinelli M Maule P Hahmann A N Gehrke O NoslashrgaringrdP B and Cutululis N A Wind and Photovoltaic Large-ScaleRegional Models for Hourly Production Evaluation IEEE TransSustain Energy 6 916ndash923 2015

Pierro M De Felice M Maggioni E Moser D Perotto ASpada F and Cornaro C Data-driven upscaling methods forregional photovoltaic power estimation and forecast using satel-lite and numerical weather prediction data Sol Energy 1581026ndash1038 2017

PV-DE register of PV plants installed in France atthe end of 2014 taken from the 4 German trans-mission system operators httpswwwtennettsodesiteTransparenzveroeffentlichungennetzkennzahlentatsaechliche-und-prognostizierte-solarenergieeinspeisunghttpwwwamprionnetphotovoltaikeinspeisung httpwww50hertzcomdeKennzahlenPhotovoltaik httpswwwtransnetbwdedekennzahlenerneuerbare-energienfotovoltaik(last access September 2016) 2014

PV-FR register of PV plants installed in Franceat the end of 2014 httpwwwstatistiquesdeveloppement-durablegouvfrenergie-climatrdifferentes-energies-energies-renouvelableshtmltx_ttnews[tt_news]=25476ampcHash=2503643552a41cb073923bec691aec022014 (last access December 2017)

Saint-Drenan Y-M A Probabilistic Approach to the Estimationof Regional Photovoltaic Power Generation using Meteorologi-cal Data Application of the Approach to the German Case PhDThesis University of Kassel 2015



Saint-Drenan Y-M Bofinger S Fritz R Vogt SGood G-H and Dobschinski J An empirical ap-proach to parameterizing photovoltaic plants for powerforecasting and simulation Sol Energy 120 479ndash493httpsdoiorg101016jsolener201507024 2015

Saint-Drenan Y-M Good G-H Braun M and Freisinger TAnalysis of the uncertainty in the estimates of regional PV powergeneration evaluated with the upscaling method Sol Energy135 536ndash550 httpsdoiorg101016jsolener2016050522016

Saint-Drenan Y-M Good G and Braun M A prob-abilistic approach to the estimation of regional photo-voltaic power production Sol Energy 147 247ndash276httpsdoiorg101016jsolener201703007 2017

Schierenbeck S Graeber D Semmig A and Weber A Ein dis-tanzbasiertes Hochrechnungsverfahren fuumlr die Einspeisung ausPhotovoltaik Energiewirtschaftliche Tagesfragen 2010

Schubert G Modeling hourly electricity generation from PV andwind plants in Europe 9th Int Conf Eur Energy Mark EEM12 1ndash7 2012

Shaker H Zareipour H and Wood D A data-driven approachfor estimating the power generation of invisible solar sites IEEET Smart Grid 99 httpsdoiorg101109TSG201525021402015

Shaker H Zareipour H and Wood D Estimating power genera-tion of invisible solar sites using publicly available data IEEET Smart Grid 99 httpsdoiorg101109TSG201625331642016

Troccoli A Goodess C Jones P Penny L Dorling SHarpham C Dubus L Parey S Claudel S Khong D-HBett P Thornton H Ranchin T Wald L Saint-Drenan Y-M De Felice M Brayshaw D Suckling E Percy B andBlower J The Copernicus Climate Change Service ldquoEuropeanClimatic Energy Mixesrdquo EMS Annual Meeting 2017 DublinIreland 4ndash8 September 2017 Abstract EMS2017-824 2017


Abstract

Introduction

Approach

Description of the model for the aggregated PV power produced in a region

Modelling the weights wi

Parameterisation of the relationship between the distribution of the orientation of PV modules and the geographical location

Implementation details

Model evaluation

Evaluation methodology

Detailed evaluation of the model output for France and Germany

Model evaluation for all European countries

Conclusions

Data availability

Competing interests

Special issue statement

Acknowledgements

References


exhaustive and time-consuming task and is intractable Al-ternatively statistical approaches may be used to train mod-els from historical time series of the aggregated PV gener-ated power such as those published by the transmission sys-tem operators In this case the collection understanding andquality check of the training data is primordial to ensure ac-curate model output Though more practical than the clas-sical approaches these statistical approaches are also timeconsuming because of the handling of the data and they can-not be applied in regions where no training data is avail-able Another common practice consists in estimating thetotal power generated in a region by upscaling the powergenerated by a subset of reference plants (Schierenbeck etal 2010 Lorenz and Heinemann 2012 Shaker et al 20152016 Saint-Drenan et al 2016 Bright et al 2017 Pierro etal 2017 Killinger et al 2017) The major obstacles to thispractice is on the one hand the establishment of criteria onthe selection of the plants that are statistically representativeof the region and their number and on the other hand theaccess to measurements of the selected plants In additionthose methods only allow estimating the PV power gener-ation for historical periods where measurements are avail-able and their extrapolation to other periods is not straight-forward This can be a major drawback for eg generationadequacy study or prospective analysis where scenarios withlong time series are needed A further option consists in se-lecting a simple PV model with a very limited number ofunknowns (Jerez et al 2015) whose implementation for anyregion is easy to do at the expense of the model accuracy Fi-nally several authors propose to consider a mix of differentkey parameters where the distributions are chosen by the au-thors (Marinelli et al 2015 Schubert 2012) This requiresa deep expertise of the domain This approach is limited to afew regions and cannot be used to model all EU countries

This brief survey of the proposed approaches demon-strates the need for a new approach that offers a bettertrade-off between implementation constraints and model out-put accuracy This paper describes a method addressing thisneed It has been developed in the framework of the EU-funded Copernicus Climate Change Service ECEM1 (Euro-pean Climate Energy Mixes) project which aims at produc-ing in close collaboration with prospective users a proof-of-concept climate service or demonstrator whose purposeis to enable the energy industry and policy makers to assesshow well different energy supply mixes in Europe will meetdemand over different time horizons (from seasonal to long-term decadal planning) focusing on the role climate has onthe mixes (Troccoli et al 2017)

The innovation of our method is the extension of theregional PV model proposed by Saint-Drenan (2015) andSaint-Drenan et al (2017) to any region without the needfor a priori knowledge of the characteristics of the installedPV plants To this end the plant-related parameters which

1httpecemclimatecopernicuseu

are needed as input to the PV model are expressed as a func-tion of known solar resource characteristics making thus themodel generalizable to any region namely beyond Germanywhere the approach was originally tested This is achieved intwo steps firstly by reducing the number of inputs to the PVmodel by the means of an analytical function for the statis-tical distribution of the module orientation and secondly byexpressing the parameters of the chosen analytical functionsas a function of known geographically-dependent informa-tion (optimal tilt angle)

The paper is organized as follows After a short summaryof the regional PV model proposed by Saint-Drenan (2015)and Saint-Drenan et al (2017) in Sect 21 the reduction ofthe number of parameters achieved by the use of an ana-lytical function is detailed in Sect 22 The approach cho-sen to relate the parameters of the analytical function toknown geographically-dependent quantities is then explainedin Sect 23 Implementation details are provided in Sect 24The results of a validation of the model are described inSect 3 where the model output has been compared to es-timates of the total PV power generation of France and Ger-many provided by transmission system operators (TSOs) Fi-nally the results and potential improvements of the approachpresented are discussed in Sect 4

2 Approach

Our approach for modelling the PV power generation in anycountry use a generic PV model which needs only the distri-bution of the two module orientation angles as inputs Thismodel is introduced in Sect 21 and the methodology for es-timating the distribution of the module orientation angles inany location is described in the Sect 22 and 23 Finallysome implementation details are given in Sect 24

21 Description of the model for the aggregated PVpower produced in a region

The proposed method is built upon previous works by Saint-Drenan (2015) and Saint-Drenan et al (2017) where a modelfor the aggregated PV power produced by a fleet of PV plantsinstalled in a region is described The authors have showedthat an accurate estimate of the German PV power genera-tion can be obtained by using the statistical distribution ofthe orientation angle of PV panels as the sole plant-relevantinput to the model (Fig 1) The model is based on the simpleidea that the aggregated PV power generated in a region isthe sum of the normalized outputs of all plants with charac-teristics Ai multiplied by the proportion wi of plants havingthe characteristics Ai in the whole set of plants installed inthe considered region The regional PV power generation cantherefore be expressed as follows

PPV(xt)=nsumi=1

wi fPV (x tG(x t) Ta (x t) Ai) (1)














wi (αiγi)=

[1radic

2πσ 2α

exp

(minus

(αi minusmicroα)2

2σ 2α

)] 1radic

2πσ 2γ

exp

(minus

(γi minusmicroγ

)22σ 2γ

) Ai = (αiγi) (2)




















respectively






wi =

intintDi

wi(αγ )dαdγ

sumi

(intintDi

wi(αγ )dαdγ

) with

Di =

[αi minus

δα

2 αi +

δα

2

]times

[γi minus

δγ

2 γi +

δγ

2

](4)



3 Model evaluation












































4 Conclusions












References

























Abstract

Introduction

Approach





Model evaluation




Conclusions

Data availability

Competing interests


Acknowledgements

References













wi (αiγi)=

[1radic

2πσ 2α

exp

(minus

(αi minusmicroα)2

2σ 2α

)] 1radic

2πσ 2γ

exp

(minus

(γi minusmicroγ

)22σ 2γ

) Ai = (αiγi) (2)




















respectively






wi =

intintDi

wi(αγ )dαdγ

sumi

(intintDi

wi(αγ )dαdγ

) with

Di =

[αi minus

δα

2 αi +

δα

2

]times

[γi minus

δγ

2 γi +

δγ

2

](4)



3 Model evaluation












































4 Conclusions












References

























Abstract

Introduction

Approach





Model evaluation




Conclusions

Data availability

Competing interests


Acknowledgements

References


















respectively






wi =

intintDi

wi(αγ )dαdγ

sumi

(intintDi

wi(αγ )dαdγ

) with

Di =

[αi minus

δα

2 αi +

δα

2

]times

[γi minus

δγ

2 γi +

δγ

2

](4)



3 Model evaluation












































4 Conclusions












References

























Abstract

Introduction

Approach





Model evaluation




Conclusions

Data availability

Competing interests


Acknowledgements

References









































4 Conclusions












References

























Abstract

Introduction

Approach





Model evaluation




Conclusions

Data availability

Competing interests


Acknowledgements

References










References

























Abstract

Introduction

Approach





Model evaluation




Conclusions

Data availability

Competing interests


Acknowledgements

References











Abstract

Introduction

Approach





Model evaluation




Conclusions

Data availability

Competing interests


Acknowledgements

References

an approach for the estimation of the aggregated …...y.-m. saint-drenan et al.: estimation of the...

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